Related Letters Pattern:

The given question consists of a series of letters arranged in a specific pattern. To solve this question, we need to identify the pattern and apply it to find the related letters.

Pattern Analysis:

Let's analyze the given series of letters:
BYCX : DWEV :: FUGT : ?

The first step is to identify the relationship between the letters in the given series. Here, we can observe that there is a cyclic shift of letters in each pair.

In the first pair, BYCX is shifted one position backward to give DWEV. The letters are shifted in the following manner:
B -> D (shifted 1 position backward)
Y -> W (shifted 1 position backward)
C -> E (shifted 1 position backward)
X -> V (shifted 1 position backward)

Similarly, we need to apply the same pattern to the second pair to find the missing letters.

Solution:

Applying the cyclic shift pattern to the second pair, FUGT, we will shift each letter one position backward:
F -> E (shifted 1 position backward)
U -> H (shifted 1 position backward)
G -> S (shifted 1 position backward)
T -> I (shifted 1 position backward)

Therefore, the missing letters in the second pair are EHSI.

Answer:

The missing letters in the series FUGT : ? are EHSI. However, none of the given options match the missing letters EHSI.

But we need to select the related letters from the given alternatives. Among the options, option 'C' (HSIR) is the most closely related to the missing letters EHSI, as it contains the same letters with a different order.

Hence, the correct answer is option 'C' (HSIR).